I checked before buying the flights and I found nothing that would have stated that "part pay with Avios" would NOT earn miles on other airlines.

Additionally, these booked to I and C class which are both AA mileage earning. So should be a clear case?

I'm suspecting that BA does not want to credit because of "part pay" but does not have anything explicit in the rules to support that.

I will post an update where there is more info available.